A Multigrid Method Based On Shifted-Inverse Power Technique for Eigenvalue Problems

TL;DR

This paper introduces a multigrid method leveraging shifted-inverse power iteration to efficiently solve eigenvalue problems by transforming them into boundary value problems on multilevel meshes, validated through numerical experiments.

Contribution

It presents a novel multigrid approach that improves eigenvalue problem solving efficiency by converting it into boundary value problems using shifted-inverse power iteration.

Findings

Enhanced computational efficiency demonstrated

Numerical experiments validate the method's effectiveness

Transforms eigenvalue problems into boundary value problems

Abstract

A multigrid method is proposed in this paper to solve eigenvalue problems by the finite element method based on the shifted-inverse power iteration technique. With this scheme, solving eigenvalue problem is transformed to a series of nonsingular solutions of boundary value problems on multilevel meshes. Since replacing the difficult eigenvalue solving by the easier solution of boundary value problems, the multigrid way can improve the overall efficiency of the eigenvalue problem solving. Some numerical experiments are presented to validate the efficiency of this new method.